Estimating rare event probability with accuracy is of great interest for safety and reliability applications. Nevertheless, some simulation parameters such as the input density parameters in the case of input-output functions, are often set for simplification reasons. A bad estimation of the parameters can strongly modify rare event probability estimations. In the present article, we design a new island particle Markov chain Monte Carlo algorithm to determine the parameters that, in case of bad estimation, tend to increase the rare event probability value. This algorithm also gives an estimate of the rare event probability maximum taking into account the likelihood of the parameter. The principles of this statistical technique are described throughout this article and its results are analyzed on different test cases.